1. Field of the Present Invention
The present invention relates to a controller, a lithographic apparatus, a method of controlling the position of an object and a method for manufacturing a device.
2. Background Art
A lithographic apparatus is a machine that applies a desired pattern onto a substrate, usually onto a target portion of the substrate. A lithographic apparatus can be used, for example, in the manufacture of integrated circuits (ICs). In that instance, a patterning device, which is alternatively referred to as a mask or a reticle, may be used to generate a circuit pattern to be formed on an individual layer of the IC. This pattern can be transferred onto a target portion (e.g., comprising part of, one, or several dies) on a substrate (e.g., a silicon wafer). Transfer of the pattern is typically via imaging onto a layer of radiation-sensitive material (resist) provided on the substrate. In general, a single substrate will contain a network of adjacent target portions that are successively patterned. Known lithographic apparatus include so-called steppers, in which each target portion is irradiated by exposing an entire pattern onto the target portion at one time, and so-called scanners, in which each target portion is irradiated by scanning the pattern through a radiation beam in a given direction (the “scanning”-direction) while synchronously scanning the substrate parallel or anti parallel to this direction. It is also possible to transfer the pattern from the patterning device to the substrate by imprinting the pattern onto the substrate.
The position and/or movement of an object in a lithographic apparatus, such as a support on which a patterning device may be supported and/or a substrate table on which a substrate may be supported, is required to be controlled very accurately. Furthermore, the object may be moved and controlled in six degrees of freedom. A control system may be provided to control an actuator system used to provide the required position and/or movement of the object.
In such a control system, resonant frequencies may result in unacceptable positioning errors. In particular, difficulties may be caused by resonant frequencies of deformation of the object itself. This may be particularly true if the position of the object is measured at a plurality of locations on the object (for example using encoders or interferometers) and two or more measurements are used to deduce another position or displacement, such as a rotation about an axis. In that case, deformation of the object may result in erroneous determination of the position of the object, depending on the actual position of the object. This in turn may feed back into the control system.
Accordingly, it may be necessary to limit the bandwidth of the control system in order to avoid stability problems induced by such resonant frequencies. This is especially true if the resonant behaviour manifests itself in the measured position in a varying manner, e.g., depending on the actual position of the object. However, lowering the bandwidth as a solution to this problem could lead to unacceptably large position errors.